Discontinuous differential equations, II

On Discontinuous Differential Equations

Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...

Discontinuous Galerkin Methods for Partial Differential Equations

Day 1: Monday, September 26, 2011 Hybridized DG Method and Mimetic Finite Differences Franco Brezzi IUSS and IMATI-CNR, Pavia Via Ferrata 1, 27100 Pavia [email protected] Abstract: The talk will discuss the relationships between certain variants of Mimetic Finite Differences and the Hybridized version of DG methods for some very simple model problem. The talk will discuss the relationships be...

First-Order Singular and Discontinuous Differential Equations

Discontinuous Ordinary Differential Equations and Stabilization

Aknowledgements I am very pleased to have the opportunity here to express my sincere thanks to Professor Bacciotti who has guided me in the study of mathematics for five years, giving me confidence and transmitting his fondness for this discipline. Particular thanks also to Professor Conti. It has been really a pleasure to attend his course in Control Theory during my first year in Firenze and ...

Efficient Algorithms for Solving Partial Differential Equations with Discontinuous Solutions

P artial differential equations (PDEs) arise in numerous scientific and engineering applications. Mathematical modeling in various applications often ends up with a set of PDEs. Mathematical techniques can help to understand many crucial properties of the PDEs, such as existence and uniqueness of solutions under suitable initial and/or boundary conditions, and the well-posedness of the problem,...